Unlocking Graphene’s Potential: Size Distribution and Topological Advances

Abstract

The size distribution and topological properties of graphene samples in two-dimensional (2D) sheets play a crucial role in various technological applications and can be characterized using multiple analytical techniques, including X-ray diffraction (XRD), Field-Emission Scanning Electron Microscopy (FESEM), Fourier-transform infrared spectroscopy (FT-IR), UV-visible spectroscopy (UV-vis), and Raman spectroscopy. In this study, we investigated the size distribution and topological features of hexagonal twisted graphene sheets and their impact on band gap energy, utilizing first-principles calculations based on Bragg's law and the Scherrer equation. Our findings demonstrate that the band gap topology of graphene sheets can be effectively modulated by introducing twisted multilayer graphene configurations.

Furthermore, the incorporation of spin-orbit coupling induces a two-band gap structure in bilayer graphene, particularly at n = 1/3 in the quantum Hall regime, significantly enhancing the potential energy of charge carriers. The measured band gaps are as follows:

- Graphene nanocrystals (GNs): 2.12 eV

- Partially reduced graphene oxide (PRGO): 0.3 – 1.5 eV

- Graphene Oxide (GO): 2.1 – 3.5 eV

Additional analyses indicate that these findings hold significant promise for the development of Field-Effect Transistors (FETs) and quantum-state superconductors, which are essential components in emerging quantum devices, including medical MRI systems, quantum computing architectures, and quantum memory storage.